The Cabinet will assemble this morning in a desperate bid to reach agreement on the matter. Fine Gael ministers last night insisted that the issue did not represent a threat to the Government and expressed their hope that consensus would be secured.

Finance Minister Michael Noonan wants the State to fight the Commission's demand that Ireland seek €13bn in back taxes from the tech giant. He rejects the ruling that Apple was the beneficiary of illegal state aid.

Just one Independent minister, Denis Naughten, has publicly said he will support the appeal.

The Independent Alliance's two TDs who attend at Cabinet, Shane Ross and Finian McGrath, held a series of meetings yesterday amid signs that a compromise could be reached.

But junior Alliance minister John Halligan caused upset when he told RTÉ he'd favour a Dáil debate on Apple before a Cabinet decision could be reached. That contradicts the position of Fine Gael who want an agreement to appeal before TDs return to the Dáil.

Sources suggested this was Mr Halligan's "very personal view" and may not pose an obstacle if a larger compromise can be reached. But the prospect of Mr Halligan quitting Government, though deemed unlikely, was not being entirely ruled out. The potential compromise turned on three requirements from the Independent Alliance and another Independent Minister, Katherine Zappone.

They are: a declaration on the future handling of multinational and other company taxes; a general statement on tax fairness; a full Dáil debate on the issue.

Officials in the Department of Finance were last night drawing up a fresh memo for Mr Noonan to bring to Cabinet today. It is understood Ms Zappone wants Mr Noonan to propose ways of ensuring Ireland has "transparent and fair taxation". A source said she "hopes to have a decision" in time for Cabinet today.

Fine Gael ministers Simon Coveney and Richard Bruton played down the split with Independent ministers.

Mr Coveney said: "Of course people have to be given the time to tease out their positions." He insisted that the Independent Alliance "don't want to destabilise the Government."

Mr Bruton said: "I don't think there is any rift. I'm very optimistic that agreement will be reached."